Last night, I took my kids out for an American children’s holiday known as Halloween.
Kids (and some ahem… adults) dress up in costume (I was a penguin this year), go door-to-door, saying “Trick or Treat” and get free candy from the neighbors.
My three kids brought back a record 420 pieces of candy. 
In today’s New York Times, I learned that in the weeks leading up to this holiday, Americans purchased $2.7 BILLION dollars in candy.
So here’s my challenge for you.
Assuming all of that candy is consumed by someone in America, estimate the total number of calories represented by $2.7 billion in candy.
Assuming 3,500 calories consumed results in a person gaining 1 lb (0.45 kg) in weight, estimate how many pounds (or kilograms) of weight the American population will gain. Add a comment below to post your entry.
The winner will receive public acknowledgement of their estimation skills, and I will send them a portion of the candy “tax” I collected from my kids.
Yes, we tax our kids for a portion of their candy collection, as mom and dad provide “infrastructure” and “chaperone” services.
It’s a useful lesson in taxation.
(We tax at a 33% tax rate.)
Mostly it is an excuse to reduce the amount of sugar they will otherwise end up consuming.
For my kids, it’s an excuse to get rid of the candy they don’t like anyways.
Good luck and Happy Halloween!
Entries will be accepted for next 72 hours, and only entries posted as comments below will be considered. A winner will be announced next week.
UPDATE as of Friday, November 4TH AT 12PM ET: New entries are welcome, but not eligible to win, as contest has closed.
329 thoughts on “A Sweet Estimation Question”
Approx. 13 million lbs
6 million kg
A typical 3.75 pound bag of candy costs 10 dollars. That’s 2.67 dollars per pound of candy or ‘a billion’ pound of candy for 2.7 billion dollars.
I assume that a child or an adult who eats candy on average will not eat an equivalent amount of other food (by weight). I.e. If a child eats a pound of candy, s/he will not eat a pound of bread or potatoes or etc.
Thus total extra calories gained = calories from candy – calories from other food
Calories Gained / pound = (calories in candy/pound) – (avg calories in food/ pound)
Calories in candy = calories in sugar = 1750Cal/pound
Avg Calories in food (based on personal exp) = 1000Cal/pound
Calories Gained/ pound = 1750-1000 = 750Cal
Total calories Gained = 750 * 1 billion = 750 billion
Total weight Gain = Total Calories Gained * pounds/Cal
Total Weight Gain = 750billion/3500 = 214.3 million pounds or about 97.2 million kg.
Assumptions:
Avg. life expectancy of 80 years – there are roughly 4 M Americans in each age group.
Avg. calories in a candy = 100.
Total candies bought = candies consumed on Halloween (70%) extra candies not consumed (30%)
Kids <=2 years don't eat candies – 0 calories
12M kids[ 3 yrs <=Age < 6 yrs ] eat 10 candies – 1000 cals/ kid
16M kids[6yrs <=Age < 10 yrs ] eat 20 candies – 2000 cals/ kid
24M kids[10yrs<=Age<=15 yrs] eat 25 candies – 2500 cals/ kid
people over 15 years don't eat candies.
Total number of calories consumed on Halloween: 12M*1000 16M*2000 24M*2500 =104000 Million calories consumed
total weight gained = 104000 Million calories /3500 = ~30 Million lbs weight gained by Americans (mostly kids).
Additionally, So, 104000 Million calories consumed ~ 1 Billon candies consumed, which is 70% of total candies bought.
So total candies bought = 1.04B/.7 ~1.4B candies.
avg. price of candies = $2.7B/1.4B ~ $2.00 / candy.
Sounds about right..
To calculate total number of calories those $2.7B candies represent:
$2.7B / average price in $ per kg of candy * % of the edible * % of nutrients that generate calories * average number of calories generated per kg of the nutrients
I’m using metrics system here. And by saying ‘edible’ I exclude stuffs that come with candy but people don’t eat such as wrapping paper.
Nutrients that generate calories in candy are carbohydrate (the major part), fat (from creme, butter, etc.), and protein (from milk, etc.). Besides them, candies also contain nutrients such as minerals (potassiums, etc.), water and others that do not generate calories.
Assumptions:
* Average price in $ per kg of candy = $20
* % of edible = 98%
* % of nutrients that generate calories = 95%
* average number of calories per kg of nutrients = 4,000
So the total calories: $2.7B / $20 * 98% * 95% * 4,000 calories = 503B calories.
And the weight gains: 503 B calories / 3,500 calories * 0.45 kg = 65M kg.
Assuming US population is 320M, on average each person gain 0.2 kg weight. Seems a little bit high for me, but we are assuming that all $2.7B is consumed, so it’s reasonable.
For question 1, we need to know 2 parameters:
1. How much kilogram candy does $2.7 billion buy?
2. How much calories does 1 kg candy have?
3. The total number of calories represented by $2.7 billion is the multiply results of the 2 numbers above.
For parameter 1:
In china, we spend 20RMB for 0.1 kg candy.
So for 1kg candy, we spend 20/0.1=200RMB=35US$.
Spend $2.7 billion we can get 2.7 billion/35=7.714*10^7 kg candy.
For parameter 2:
The 0.1 kg candy represents 3000 kJ energy, which means in 1 kg candy there is 3000 kJ/0.1 kg=30000 kJ=30000*242=7.26*10^6 cal.
The total number of calories represented by $2.7billion is:
7.714*107*7.26*106=5.86*1014 cal =58600 billion cal
For question 2, we use the total calories represented by $2.7 billion divide the 3500 cal/1 lb:
Pounds of weight the American population will gain=5.86*1014/3500=1.67*1011 lb=167billion lb
Wow, so for me I think the key point is figuring out the amount of calory for each candy (considering the amount could be varied from 200 to 1000), and also the unit cost for each candy purchased.
1, since the amount of calory for each candy could be varied from 200 to 1000, I prefer put an average of 600 as the amount of calory for each candy consumed;
2, Assume the unit cost for each candy is around $2 (not sure if it’s reasonable)
3, since we already have the total amount of purchase (2.7 Billion), and we have the unit cost for each candy ($2 approximately), then we can calculate the total number of candies consumed = 2.7 Billion/$2=1.35 Billion
4, with the estimated amount of calory for each candy (600), we can get the number of total calories consumed = 810 Billion Calories
5, Then we divide the total number of calories consumed by 3500 to get the result that how many pounds that the American population gain:
810 Billion/3500=231.43M lb
To check if this number is reasonable, let’s assume the total number of American population is 320M, we can calculate the weight that each Amercian Population gain=231.43M/320M=0.7232 lb.
Seems like reasonable and I will assume my assumpation for the unit cost of candy is also kind-of reasonable ^_^
Splitting the candies into 2 types – Chocolate minies, Non-chocolate candies
Chocolate minies (like Hershy, Twix, Mars etc)
Average price of $10 for 2Lb (900 g) pack (roughly 100 miny bars)
Average calorie per miny-bar 40
Average calorie per 2Lb pack = 40*100 = 4KCal
Non-chocolate candies (Like Jelly belly, Skittles etc)
Average price of $8 for 2Lb pack (roughly 60 miny packets)
Average calorie per miny-pack 25
Average calorie per 2Lb pack = 25*60 = 1.5Kcal
Knowing that the chocoloate candies are more popular among kids and are more easily available, lets assume that 70% of the sales were from these and the remaining 30% was from non-chocolate candies.
That means,
Dollar sales from chcolate candies = 2.7B * 70% = 1.9B => 1.9B/10 = 190M packs of 2LB each
Calories from chcolate candies = 190M * 4KCal = 760M Kcal
Dollar sales from non-chcolate candies = 2.7B * 30% = 0.8B => 0.8B/8 = 100M packs of 2LB each
Calories from chcolate candies = 100M * 1.5Kcal = 150M Kcal
Total calories = 760 150 = 910M Kcal
Pounds gained = 910M Kcal/3.5Kcal = 260 Million pounds
From your picture, there are three categories of candies and assuming this is representative of all candies collected:
Chocolate: 80%
Sugar Candies: 15%
Others: 5%
Assuming price/pound:
Chocolate: $5
Sugar Candies: $4
Others: $8
Assuming calorie/pound:
Chocolate: 2500
Sugar Candies: 1500
Others: 1000
Weighted average price/pound:
80%*5 15%*4 5%*8=$5
Weighted average calories/pound:
80%*2500 15%*1500 5%*1000=2275
Total calories:
$2.7B/$5*2275=$0.54B*2275=approx 1210Billion
Total pounds gained:
1210Billion/3500=approx350M
Assuming US population is 350M, this is approx 1pounds per person. Were all the candies consumed by American kids, assuming kids interested in candies range from age 3 to 13 and American’s life expectancy is 80, then that is 8 pounds per kid!
Thankfully, some candies are bought back and redistributed after Halloween.
http://www.seattletimes.com/nation-world/the-day-after-halloween-where-does-all-the-candy-go/
152M Pounds!
total candies purchased during Halloween: $2,700,000,000
assuming 1 candy cost :$1
total candies : 2,700,000,000 candies
assuming candy bar calories/ 100 grams : 400 cal
1 candy bar weight : 50 grams
average 1 candy bar calories : 200 cal
1 calory will gain : 0.13 grams
total calories from puchased candies: 540,000,000,000 calories
total gain (grams) from candies purchased : 70,200,000,000 grams
in kg 70,200,000 (70.2 million kg weight gains)